The midfielder, 19, made his first-team debut for the club on the opening day of the season as he stepped off the bench in the 3-2 win at Crystal Palace, and manager Gianfranco Zola has been impressed with what he has seen of the youngster.
Smith, whose deal also includes the option of a further 12 months, follows in the footsteps of fellow hot prospects Sean Murray and Tommie Hoban by penning a long-term deal.
Zola told the club's official website: "Connor is one of the young players who really impressed us straight away.
"You can see he is a midfielder who has a good eye for a goal, physically he is very good and technically as well. He is the type of midfielder that can be good at defending and also coming forward so we value him highly."